Dynamical inverse problem for the discrete Schrödinger operator

Abstract

We consider the inverse problem for the dynamical system with discrete Schrödinger operator and discrete time. As an inverse data we take a \emph{response operator}, the natural analog of the dynamical Dirichlet-to-Neumann map. We derive two types of equations of inverse problem and answer a question on the characterization of the inverse data, i.e. we describe the set of operators, which are \emph{response operators} of the dynamical system governed by the discrete Schrödinger operator.

References in corpus (2)

• The boundary control approach to inverse spectral theory
• Unified approach to classical equations of inverse problem theory

Cited by in corpus (5)

• On the relationship between Weyl functions of Jacobi matrices and response vectors for special dynamical systems with discrete time
• Forward and inverse problems for a finite Krein-Stieltjes string. Approximation of constant density by point masses
• Construction of solutions of Toda lattices by the classical moment problem
• Inverse problems for finite Jacobi matrices and Krein--Stieltjes strings
• Discrete dynamical systems: inverse problems and related topics